Covariate Information Matrix for Sufficient Dimension Reduction

• 成果类型: Article
• 署名作者: Yao, Weixin; Nandy, Debmalya; Lindsay, Bruce G.; Chiaromonte, Francesca
• 署名单位: University of California System; University of California Riverside; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Scuola Superiore Sant'Anna; Scuola Superiore Sant'Anna
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1515080
• 发表日期: 2019
• 页码: 1752-1764
• 关键词: sliced inverse regression; Independent Component Analysis; projection pursuit; central subspace; algorithm; selection

摘要

Building upon recent research on the applications of the density information matrix, we develop a tool for sufficient dimension reduction (SDR) in regression problems called covariate information matrix (CIM). CIM exhaustively identifies the central subspace (CS) and provides a rank ordering of the reduced covariates in terms of their regression information. Compared to other popular SDR methods, CIM does not require distributional assumptions on the covariates, or estimation of the mean regression function. CIM is implemented via eigen-decomposition of a matrix estimated with a previously developed efficient nonparametric density estimation technique. We also propose a bootstrap-based diagnostic plot for estimating the dimension of the CS. Results of simulations and real data applications demonstrate superior or competitive performance of CIM compared to that of some other SDR methods. for this article are available online.